library(tidyverse)  # Manipulation des données
library(readxl)     # Lecture des fichiers Excel
library(ggpubr)     # Représentations graphiques
library(rstatix)    # Tests statistiques en langage Dplyr
library(corrplot)   # Corrélogrammes
library(plotly)     # Graphes intéractifs
library(psych)
library(EFAtools)
library(shiny)

Avec toutes les variables quantitatives

Données

Pré-requis

Bartlett

bartlett.test(dataComp %>% select(where(is.numeric)))

    Bartlett test of homogeneity of variances

data:  dataComp %>% select(where(is.numeric))
Bartlett's K-squared = 564.07, df = 41, p-value < 2.2e-16

KMO

KMO(dataComp %>% select(where(is.numeric)))
ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

── Kaiser-Meyer-Olkin criterion (KMO) ────────────────────────────────────

✔ The overall KMO value for your data is meritorious.
  These data are probably suitable for factor analysis.

  Overall: 0.841

  For each variable:
 AFE1  AFE2  AFE4  AFE5  AFP1  AFP2  AFP3  AFP4  AFP5  AFP6   CF1   CF2 
0.772 0.401 0.741 0.577 0.881 0.791 0.909 0.883 0.850 0.887 0.922 0.775 
  CF3   CF4   CF5   CF6   CF7   CF8 IEIP1 IEIP2 IEIP3 IEIP4  LDS1  LDS2 
0.836 0.845 0.877 0.889 0.928 0.844 0.760 0.899 0.876 0.584 0.398 0.831 
 LDS3  LDS4  LDS5  LDS6  MOT1 MOT21  MOT3  MOT4  MOT5  MOT6  MOT7  MOT8 
0.644 0.726 0.508 0.668 0.870 0.905 0.916 0.883 0.912 0.847 0.923 0.884 
 MOT9 NSUB1 NSUB2 NSUB3 NSUB4 NSUB5 
0.907 0.580 0.678 0.490 0.555 0.751 

Nombre de facteurs

fa.parallel(dataComp, fa="fa", fm="pa")
Parallel analysis suggests that the number of factors =  7  and the number of components =  NA 

Modélisation

2 Facteurs

Modèle

fit2 <- fa(dataComp, nfactors = 2, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit2)
Factor Analysis using method =  pa
Call: fa(r = dataComp, nfactors = 2, rotate = "oblimin", fm = "pa", 
    use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix

                       PA1  PA2
SS loadings           7.61 3.67
Proportion Var        0.18 0.09
Cumulative Var        0.18 0.27
Proportion Explained  0.67 0.33
Cumulative Proportion 0.67 1.00

 With factor correlations of 
     PA1  PA2
PA1 1.00 0.54
PA2 0.54 1.00

Mean item complexity =  1.3
Test of the hypothesis that 2 factors are sufficient.

The degrees of freedom for the null model are  861  and the objective function was  18.17 with Chi Square of  3037.23
The degrees of freedom for the model are 778  and the objective function was  7.89 

The root mean square of the residuals (RMSR) is  0.07 
The df corrected root mean square of the residuals is  0.08 

The harmonic number of observations is  183 with the empirical chi square  1683.87  with prob <  9.4e-69 
The total number of observations was  183  with Likelihood Chi Square =  1308.74  with prob <  1.2e-29 

Tucker Lewis Index of factoring reliability =  0.727
RMSEA index =  0.061  and the 90 % confidence intervals are  0.055 0.067
BIC =  -2744.24
Fit based upon off diagonal values = 0.91
Measures of factor score adequacy             
                                                   PA1  PA2
Correlation of (regression) scores with factors   0.96 0.93
Multiple R square of scores with factors          0.92 0.86
Minimum correlation of possible factor scores     0.85 0.72

Loadings

print(fit2$loadings, sort = T, cutoff = 0.4)

Loadings:
      PA1    PA2   
AFP3   0.649       
AFP4   0.531       
AFP5   0.581       
CF4    0.767       
CF5    0.592       
CF7    0.584       
IEIP2  0.733       
IEIP3  0.548       
MOT21  0.535       
MOT3   0.657       
MOT7   0.536       
MOT8   0.621       
MOT9   0.543       
AFP1          0.728
AFP2          0.591
AFP6          0.744
CF6           0.521
AFE1               
AFE2               
AFE4               
AFE5         -0.426
CF1           0.469
CF2                
CF3    0.457       
CF8                
IEIP1              
IEIP4              
LDS1               
LDS2               
LDS3               
LDS4               
LDS5               
LDS6               
MOT1               
MOT4   0.492       
MOT5   0.489       
MOT6   0.495       
NSUB1              
NSUB2        -0.411
NSUB3              
NSUB4              
NSUB5  0.465       

                 PA1   PA2
SS loadings    7.190 3.250
Proportion Var 0.171 0.077
Cumulative Var 0.171 0.249

Diagramme

fa.diagram(fit2, digits = 2)

3 Facteurs

Modèle

fit3 <- fa(dataComp, nfactors = 3, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit3)
Factor Analysis using method =  pa
Call: fa(r = dataComp, nfactors = 3, rotate = "oblimin", fm = "pa", 
    use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix

                       PA1  PA2  PA3
SS loadings           7.54 3.72 1.63
Proportion Var        0.18 0.09 0.04
Cumulative Var        0.18 0.27 0.31
Proportion Explained  0.58 0.29 0.13
Cumulative Proportion 0.58 0.87 1.00

 With factor correlations of 
      PA1   PA2   PA3
PA1  1.00  0.50 -0.12
PA2  0.50  1.00 -0.04
PA3 -0.12 -0.04  1.00

Mean item complexity =  1.6
Test of the hypothesis that 3 factors are sufficient.

The degrees of freedom for the null model are  861  and the objective function was  18.17 with Chi Square of  3037.23
The degrees of freedom for the model are 738  and the objective function was  7 

The root mean square of the residuals (RMSR) is  0.06 
The df corrected root mean square of the residuals is  0.07 

The harmonic number of observations is  183 with the empirical chi square  1267.66  with prob <  1.4e-30 
The total number of observations was  183  with Likelihood Chi Square =  1155.88  with prob <  5.2e-21 

Tucker Lewis Index of factoring reliability =  0.772
RMSEA index =  0.055  and the 90 % confidence intervals are  0.05 0.062
BIC =  -2688.72
Fit based upon off diagonal values = 0.93
Measures of factor score adequacy             
                                                   PA1  PA2  PA3
Correlation of (regression) scores with factors   0.96 0.93 0.83
Multiple R square of scores with factors          0.92 0.87 0.69
Minimum correlation of possible factor scores     0.84 0.73 0.38

Loadings

print(fit3$loadings, sort = T, cutoff = 0.4)

Loadings:
      PA1    PA2    PA3   
AFP3   0.639              
AFP4   0.528              
AFP5   0.572              
CF4    0.758              
CF5    0.586              
CF7    0.574              
IEIP2  0.718              
IEIP3  0.541              
MOT21  0.529              
MOT3   0.648              
MOT6   0.504              
MOT7   0.529              
MOT8   0.621              
MOT9   0.539              
AFP1          0.704       
AFP2          0.665       
AFP6          0.776       
NSUB1               -0.532
AFE1                      
AFE2                      
AFE4                      
AFE5                      
CF1           0.473       
CF2                       
CF3    0.449              
CF6           0.476       
CF8                       
IEIP1                     
IEIP4                     
LDS1                      
LDS2                -0.410
LDS3                      
LDS4                      
LDS5                 0.423
LDS6                      
MOT1                      
MOT4   0.484              
MOT5   0.485              
NSUB2                     
NSUB3                     
NSUB4                     
NSUB5  0.457              

                 PA1   PA2   PA3
SS loadings    7.048 3.224 1.620
Proportion Var 0.168 0.077 0.039
Cumulative Var 0.168 0.245 0.283

Diagramme

fa.diagram(fit3, digits = 2)

4 Facteurs

Modèle

fit4 <- fa(dataComp, nfactors = 4, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit4)
Factor Analysis using method =  pa
Call: fa(r = dataComp, nfactors = 4, rotate = "oblimin", fm = "pa", 
    use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix

                       PA1  PA2  PA3  PA4
SS loadings           6.60 3.87 1.98 1.93
Proportion Var        0.16 0.09 0.05 0.05
Cumulative Var        0.16 0.25 0.30 0.34
Proportion Explained  0.46 0.27 0.14 0.13
Cumulative Proportion 0.46 0.73 0.87 1.00

 With factor correlations of 
     PA1  PA2  PA3  PA4
PA1 1.00 0.48 0.29 0.20
PA2 0.48 1.00 0.18 0.17
PA3 0.29 0.18 1.00 0.07
PA4 0.20 0.17 0.07 1.00

Mean item complexity =  1.7
Test of the hypothesis that 4 factors are sufficient.

The degrees of freedom for the null model are  861  and the objective function was  18.17 with Chi Square of  3037.23
The degrees of freedom for the model are 699  and the objective function was  6.14 

The root mean square of the residuals (RMSR) is  0.05 
The df corrected root mean square of the residuals is  0.06 

The harmonic number of observations is  183 with the empirical chi square  950.26  with prob <  6.5e-10 
The total number of observations was  183  with Likelihood Chi Square =  1010.64  with prob <  9.1e-14 

Tucker Lewis Index of factoring reliability =  0.82
RMSEA index =  0.049  and the 90 % confidence intervals are  0.043 0.056
BIC =  -2630.79
Fit based upon off diagonal values = 0.95
Measures of factor score adequacy             
                                                   PA1  PA2  PA3  PA4
Correlation of (regression) scores with factors   0.96 0.93 0.86 0.85
Multiple R square of scores with factors          0.92 0.87 0.74 0.72
Minimum correlation of possible factor scores     0.83 0.74 0.48 0.45

Loadings

print(fit4$loadings, sort = T, cutoff = 0.4)

Loadings:
      PA1    PA2    PA3    PA4   
AFP3   0.653                     
AFP4   0.710                     
AFP5   0.622                     
CF4    0.688                     
CF5    0.548                     
IEIP2  0.631                     
MOT3   0.612                     
MOT5   0.508                     
MOT7   0.535                     
MOT8   0.802                     
AFP1          0.695              
AFP2          0.711              
AFP6          0.790              
LDS2                 0.562       
LDS3                 0.620       
NSUB1                0.564       
AFE1                             
AFE2                             
AFE4                             
AFE5                        0.409
CF1           0.487              
CF2                              
CF3                              
CF6           0.442              
CF7                              
CF8                              
IEIP1                            
IEIP3  0.433                     
IEIP4                       0.459
LDS1                             
LDS4                 0.456       
LDS5                             
LDS6                             
MOT1          0.423              
MOT21  0.472                     
MOT4                        0.442
MOT6   0.493                     
MOT9   0.486                     
NSUB2                            
NSUB3                       0.474
NSUB4                            
NSUB5                            

                 PA1   PA2   PA3   PA4
SS loadings    5.869 3.306 1.826 1.768
Proportion Var 0.140 0.079 0.043 0.042
Cumulative Var 0.140 0.218 0.262 0.304

Diagramme

fa.diagram(fit4, digits = 2)

5 Facteurs

Modèle

fit5 <- fa(dataComp, nfactors = 5, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit5)
Factor Analysis using method =  pa
Call: fa(r = dataComp, nfactors = 5, rotate = "oblimin", fm = "pa", 
    use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix

                       PA1  PA2  PA4  PA3  PA5
SS loadings           6.47 3.35 2.19 2.09 1.43
Proportion Var        0.15 0.08 0.05 0.05 0.03
Cumulative Var        0.15 0.23 0.29 0.34 0.37
Proportion Explained  0.42 0.22 0.14 0.13 0.09
Cumulative Proportion 0.42 0.63 0.77 0.91 1.00

 With factor correlations of 
     PA1   PA2  PA4  PA3   PA5
PA1 1.00  0.45 0.26 0.31  0.01
PA2 0.45  1.00 0.27 0.20 -0.05
PA4 0.26  0.27 1.00 0.09  0.02
PA3 0.31  0.20 0.09 1.00  0.02
PA5 0.01 -0.05 0.02 0.02  1.00

Mean item complexity =  1.8
Test of the hypothesis that 5 factors are sufficient.

The degrees of freedom for the null model are  861  and the objective function was  18.17 with Chi Square of  3037.23
The degrees of freedom for the model are 661  and the objective function was  5.51 

The root mean square of the residuals (RMSR) is  0.05 
The df corrected root mean square of the residuals is  0.06 

The harmonic number of observations is  183 with the empirical chi square  770.08  with prob <  0.0021 
The total number of observations was  183  with Likelihood Chi Square =  903.09  with prob <  9.7e-10 

Tucker Lewis Index of factoring reliability =  0.851
RMSEA index =  0.044  and the 90 % confidence intervals are  0.037 0.052
BIC =  -2540.38
Fit based upon off diagonal values = 0.96
Measures of factor score adequacy             
                                                   PA1  PA2  PA4  PA3
Correlation of (regression) scores with factors   0.96 0.93 0.87 0.87
Multiple R square of scores with factors          0.92 0.86 0.75 0.75
Minimum correlation of possible factor scores     0.83 0.72 0.50 0.50
                                                   PA5
Correlation of (regression) scores with factors   0.83
Multiple R square of scores with factors          0.69
Minimum correlation of possible factor scores     0.37

Loadings

print(fit5$loadings, sort = T, cutoff = 0.4)

Loadings:
      PA1    PA2    PA4    PA3    PA5   
AFP3   0.644                            
AFP4   0.708                            
AFP5   0.613                            
CF4    0.692                            
CF5    0.540                            
IEIP2  0.630                            
MOT3   0.601                            
MOT5   0.500                            
MOT7   0.528                            
MOT8   0.785                            
AFE1          0.647                     
AFP1          0.733                     
AFP2          0.735                     
AFP6          0.654                     
MOT4                 0.513              
LDS2                        0.562       
LDS3                        0.628       
NSUB1                       0.548       
AFE5                               0.519
NSUB3                              0.516
AFE2                                    
AFE4                                    
CF1           0.430                     
CF2                                     
CF3                                     
CF6           0.489                     
CF7                                     
CF8                                     
IEIP1                                   
IEIP3  0.427                            
IEIP4                                   
LDS1                                    
LDS4                        0.475       
LDS5                                    
LDS6                 0.423              
MOT1                 0.428              
MOT21  0.463                            
MOT6   0.481                            
MOT9   0.478                            
NSUB2                              0.442
NSUB4                                   
NSUB5                                   

                 PA1   PA2   PA4   PA3   PA5
SS loadings    5.725 2.823 1.815 1.890 1.415
Proportion Var 0.136 0.067 0.043 0.045 0.034
Cumulative Var 0.136 0.204 0.247 0.292 0.325

Diagramme

fa.diagram(fit5, digits = 2)

6 Facteurs

Modèle

fit6 <- fa(dataComp, nfactors = 6, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit6)
Factor Analysis using method =  pa
Call: fa(r = dataComp, nfactors = 6, rotate = "oblimin", fm = "pa", 
    use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix

                       PA1  PA2  PA4  PA3  PA5  PA6
SS loadings           4.75 3.43 3.30 2.19 1.45 1.38
Proportion Var        0.11 0.08 0.08 0.05 0.03 0.03
Cumulative Var        0.11 0.19 0.27 0.33 0.36 0.39
Proportion Explained  0.29 0.21 0.20 0.13 0.09 0.08
Cumulative Proportion 0.29 0.50 0.70 0.83 0.92 1.00

 With factor correlations of 
     PA1   PA2  PA4  PA3   PA5  PA6
PA1 1.00  0.39 0.45 0.27  0.00 0.06
PA2 0.39  1.00 0.38 0.22 -0.05 0.17
PA4 0.45  0.38 1.00 0.24  0.06 0.17
PA3 0.27  0.22 0.24 1.00  0.01 0.01
PA5 0.00 -0.05 0.06 0.01  1.00 0.01
PA6 0.06  0.17 0.17 0.01  0.01 1.00

Mean item complexity =  2.2
Test of the hypothesis that 6 factors are sufficient.

The degrees of freedom for the null model are  861  and the objective function was  18.17 with Chi Square of  3037.23
The degrees of freedom for the model are 624  and the objective function was  5.01 

The root mean square of the residuals (RMSR) is  0.05 
The df corrected root mean square of the residuals is  0.05 

The harmonic number of observations is  183 with the empirical chi square  639.66  with prob <  0.32 
The total number of observations was  183  with Likelihood Chi Square =  816.82  with prob <  2.9e-07 

Tucker Lewis Index of factoring reliability =  0.874
RMSEA index =  0.041  and the 90 % confidence intervals are  0.033 0.049
BIC =  -2433.89
Fit based upon off diagonal values = 0.96
Measures of factor score adequacy             
                                                   PA1  PA2  PA4  PA3
Correlation of (regression) scores with factors   0.94 0.93 0.90 0.87
Multiple R square of scores with factors          0.88 0.86 0.82 0.76
Minimum correlation of possible factor scores     0.76 0.72 0.64 0.53
                                                   PA5  PA6
Correlation of (regression) scores with factors   0.83 0.83
Multiple R square of scores with factors          0.69 0.68
Minimum correlation of possible factor scores     0.38 0.36

Loadings

print(fit6$loadings, sort = T, cutoff = 0.4)

Loadings:
      PA1    PA2    PA4    PA3    PA5    PA6   
AFP4   0.671                                   
AFP5   0.547                                   
CF4    0.525                                   
MOT3   0.509                                   
MOT7   0.518                                   
MOT8   0.738                                   
AFE1          0.670                            
AFP1          0.732                            
AFP2          0.719                            
AFP6          0.639                            
CF6           0.514                            
IEIP3                0.595                     
NSUB5                0.581                     
LDS2                        0.581              
LDS3                        0.640              
NSUB1                       0.543              
AFE5                               0.526       
LDS6                                      0.509
AFE2                                           
AFE4                                           
AFP3   0.400         0.462                     
CF1           0.432                            
CF2                                            
CF3                                            
CF5                                            
CF7                                            
CF8                                            
IEIP1                                          
IEIP2  0.447                                   
IEIP4                                          
LDS1                                           
LDS4                        0.467              
LDS5                                           
MOT1                                           
MOT21                                          
MOT4                 0.460                     
MOT5                                           
MOT6   0.448                                   
MOT9                 0.470                     
NSUB2                              0.460       
NSUB3                              0.495       
NSUB4                                          

                 PA1   PA2   PA4   PA3   PA5   PA6
SS loadings    3.875 2.851 2.477 1.956 1.432 1.252
Proportion Var 0.092 0.068 0.059 0.047 0.034 0.030
Cumulative Var 0.092 0.160 0.219 0.266 0.300 0.330

Diagramme

fa.diagram(fit6, digits = 2)

7 Facteurs

Modèle

fit7 <- fa(dataComp, nfactors = 7, rotate = "oblimin", fm = "pa", use = "pairwise")
Warning: convergence not obtained in GPFoblq. 1000 iterations used.
print(fit7)
Factor Analysis using method =  pa
Call: fa(r = dataComp, nfactors = 7, rotate = "oblimin", fm = "pa", 
    use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix

                       PA1  PA7  PA2  PA3  PA5  PA6  PA4
SS loadings           4.35 3.62 3.20 1.81 1.54 1.51 1.41
Proportion Var        0.10 0.09 0.08 0.04 0.04 0.04 0.03
Cumulative Var        0.10 0.19 0.27 0.31 0.35 0.38 0.42
Proportion Explained  0.25 0.21 0.18 0.10 0.09 0.09 0.08
Cumulative Proportion 0.25 0.46 0.64 0.74 0.83 0.92 1.00

 With factor correlations of 
     PA1  PA7   PA2   PA3   PA5  PA6   PA4
PA1 1.00 0.54  0.35  0.19  0.08 0.26  0.06
PA7 0.54 1.00  0.40  0.17  0.11 0.24  0.13
PA2 0.35 0.40  1.00  0.14 -0.01 0.22  0.13
PA3 0.19 0.17  0.14  1.00  0.03 0.14 -0.02
PA5 0.08 0.11 -0.01  0.03  1.00 0.06  0.04
PA6 0.26 0.24  0.22  0.14  0.06 1.00  0.07
PA4 0.06 0.13  0.13 -0.02  0.04 0.07  1.00

Mean item complexity =  2.3
Test of the hypothesis that 7 factors are sufficient.

The degrees of freedom for the null model are  861  and the objective function was  18.17 with Chi Square of  3037.23
The degrees of freedom for the model are 588  and the objective function was  4.49 

The root mean square of the residuals (RMSR) is  0.04 
The df corrected root mean square of the residuals is  0.05 

The harmonic number of observations is  183 with the empirical chi square  522.59  with prob <  0.98 
The total number of observations was  183  with Likelihood Chi Square =  730.28  with prob <  5.4e-05 

Tucker Lewis Index of factoring reliability =  0.9
RMSEA index =  0.036  and the 90 % confidence intervals are  0.027 0.045
BIC =  -2332.9
Fit based upon off diagonal values = 0.97
Measures of factor score adequacy             
                                                   PA1  PA7  PA2  PA3
Correlation of (regression) scores with factors   0.94 0.92 0.93 0.86
Multiple R square of scores with factors          0.88 0.86 0.86 0.74
Minimum correlation of possible factor scores     0.75 0.71 0.71 0.47
                                                   PA5  PA6  PA4
Correlation of (regression) scores with factors   0.84 0.82 0.84
Multiple R square of scores with factors          0.71 0.67 0.70
Minimum correlation of possible factor scores     0.41 0.33 0.40

Loadings

print(fit7$loadings, sort = T, cutoff = 0.4)

Loadings:
      PA1    PA7    PA2    PA3    PA5    PA6    PA4   
AFP4   0.608                                          
AFP5   0.646                                          
MOT21  0.501                                          
MOT7   0.561                                          
MOT8   0.778                                          
IEIP3         0.516                                   
MOT9          0.745                                   
AFE1                 0.610                            
AFP1                 0.721                            
AFP2                 0.738                            
AFP6                 0.653                            
LDS3                        0.521                     
NSUB1                       0.622                     
AFE5                               0.503              
NSUB3                              0.542              
AFE2                                                  
AFE4                                                  
AFP3          0.472                                   
CF1                                                   
CF2                                                   
CF3                                       0.445       
CF4                                                   
CF5           0.458                                   
CF6           0.400  0.425                            
CF7                                                   
CF8                                                   
IEIP1                                                 
IEIP2  0.454                                          
IEIP4                                                 
LDS1                                                  
LDS2                        0.442                     
LDS4                        0.499                     
LDS5                       -0.457                     
LDS6                                             0.440
MOT1          0.403                                   
MOT3                                                  
MOT4                                                  
MOT5                                                  
MOT6   0.480                                          
NSUB2                              0.442              
NSUB4                                                 
NSUB5                                                 

                 PA1   PA7   PA2   PA3   PA5   PA6   PA4
SS loadings    3.478 2.690 2.678 1.683 1.500 1.227 1.304
Proportion Var 0.083 0.064 0.064 0.040 0.036 0.029 0.031
Cumulative Var 0.083 0.147 0.211 0.251 0.286 0.316 0.347

Diagramme

fa.diagram(fit7, digits = 2)

Fiabilité

alpha(dataComp)
Warning: Some items were negatively correlated with the total scale and probably 
should be reversed.  
To do this, run the function again with the 'check.keys=TRUE' option
Some items ( AFE5 LDS5 NSUB2 ) were negatively correlated with the total scale and 
probably should be reversed.  
To do this, run the function again with the 'check.keys=TRUE' option
Reliability analysis   
Call: alpha(x = dataComp)

 

    95% confidence boundaries 

 Reliability if an item is dropped:

 Item statistics 

Non missing response frequency for each item
         1    2    3    4    5 miss
AFE1  0.03 0.07 0.50 0.21 0.18    0
AFE2  0.08 0.18 0.41 0.22 0.11    0
AFE4  0.05 0.09 0.15 0.28 0.43    0
AFE5  0.21 0.39 0.22 0.14 0.04    0
AFP1  0.02 0.08 0.50 0.24 0.16    0
AFP2  0.08 0.12 0.47 0.22 0.11    0
AFP3  0.01 0.05 0.15 0.34 0.46    0
AFP4  0.01 0.02 0.06 0.36 0.56    0
AFP5  0.01 0.02 0.10 0.28 0.58    0
AFP6  0.02 0.07 0.49 0.30 0.12    0
CF1   0.02 0.03 0.13 0.45 0.37    0
CF2   0.07 0.34 0.25 0.27 0.08    0
CF3   0.02 0.03 0.13 0.30 0.53    0
CF4   0.01 0.02 0.05 0.27 0.64    0
CF5   0.01 0.01 0.04 0.35 0.59    0
CF6   0.03 0.09 0.36 0.27 0.26    0
CF7   0.02 0.04 0.21 0.46 0.27    0
CF8   0.04 0.13 0.26 0.43 0.13    0
IEIP1 0.01 0.01 0.03 0.47 0.49    0
IEIP2 0.02 0.03 0.07 0.28 0.60    0
IEIP3 0.02 0.08 0.18 0.38 0.34    0
IEIP4 0.10 0.11 0.28 0.31 0.20    0
LDS1  0.42 0.58 0.00 0.00 0.00    0
LDS2  0.04 0.07 0.25 0.43 0.21    0
LDS3  0.02 0.07 0.67 0.19 0.05    0
LDS4  0.04 0.10 0.52 0.27 0.07    0
LDS5  0.17 0.31 0.34 0.15 0.03    0
LDS6  0.04 0.20 0.38 0.22 0.15    0
MOT1  0.02 0.08 0.46 0.30 0.14    0
MOT21 0.01 0.02 0.10 0.58 0.29    0
MOT3  0.01 0.02 0.04 0.50 0.44    0
MOT4  0.04 0.10 0.40 0.30 0.16    0
MOT5  0.01 0.04 0.22 0.48 0.25    0
MOT6  0.02 0.00 0.02 0.26 0.70    0
MOT7  0.01 0.01 0.09 0.46 0.44    0
MOT8  0.01 0.01 0.01 0.29 0.69    0
MOT9  0.03 0.02 0.16 0.39 0.40    0
NSUB1 0.02 0.03 0.41 0.39 0.15    0
NSUB2 0.12 0.32 0.46 0.09 0.02    0
NSUB3 0.22 0.32 0.25 0.17 0.04    0
NSUB4 0.11 0.16 0.26 0.31 0.16    0
NSUB5 0.05 0.08 0.23 0.38 0.25    0

Avec le retrait : AFE, NSUB, LDS

Données

Pré-requis

Bartlett

bartlett.test(dataComp %>% select(where(is.numeric)))

    Bartlett test of homogeneity of variances

data:  dataComp %>% select(where(is.numeric))
Bartlett's K-squared = 292.4, df = 26, p-value < 2.2e-16

KMO

KMO(dataComp %>% select(where(is.numeric)))
ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

── Kaiser-Meyer-Olkin criterion (KMO) ────────────────────────────────────

✔ The overall KMO value for your data is marvellous.
  These data are probably suitable for factor analysis.

  Overall: 0.907

  For each variable:
 AFP1  AFP2  AFP3  AFP4  AFP5  AFP6   CF1   CF2   CF3   CF4   CF5   CF6 
0.886 0.807 0.929 0.908 0.895 0.878 0.945 0.823 0.829 0.873 0.927 0.916 
  CF7   CF8 IEIP1 IEIP2 IEIP3 IEIP4  MOT1 MOT21  MOT3  MOT4  MOT5  MOT6 
0.930 0.893 0.842 0.931 0.929 0.635 0.877 0.923 0.938 0.889 0.942 0.920 
 MOT7  MOT8  MOT9 
0.956 0.901 0.926 

Nombre de facteurs

fa.parallel(dataComp, fa="fa", fm="pa")
Parallel analysis suggests that the number of factors =  3  and the number of components =  NA 

Modélisation

2 Facteurs

Modèle

fit2 <- fa(dataComp, nfactors = 2, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit2)
Factor Analysis using method =  pa
Call: fa(r = dataComp, nfactors = 2, rotate = "oblimin", fm = "pa", 
    use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix

                       PA1  PA2
SS loadings           7.03 3.14
Proportion Var        0.26 0.12
Cumulative Var        0.26 0.38
Proportion Explained  0.69 0.31
Cumulative Proportion 0.69 1.00

 With factor correlations of 
     PA1  PA2
PA1 1.00 0.51
PA2 0.51 1.00

Mean item complexity =  1.2
Test of the hypothesis that 2 factors are sufficient.

The degrees of freedom for the null model are  351  and the objective function was  12.18 with Chi Square of  2097.64
The degrees of freedom for the model are 298  and the objective function was  2.83 

The root mean square of the residuals (RMSR) is  0.06 
The df corrected root mean square of the residuals is  0.06 

The harmonic number of observations is  183 with the empirical chi square  423.43  with prob <  2.3e-06 
The total number of observations was  183  with Likelihood Chi Square =  483.61  with prob <  5.4e-11 

Tucker Lewis Index of factoring reliability =  0.874
RMSEA index =  0.058  and the 90 % confidence intervals are  0.049 0.068
BIC =  -1068.82
Fit based upon off diagonal values = 0.97
Measures of factor score adequacy             
                                                   PA1  PA2
Correlation of (regression) scores with factors   0.96 0.93
Multiple R square of scores with factors          0.92 0.87
Minimum correlation of possible factor scores     0.84 0.74

Loadings

print(fit2$loadings, sort = T, cutoff = 0.4)

Loadings:
      PA1    PA2   
AFP3   0.661       
AFP4   0.623       
AFP5   0.606       
CF4    0.780       
CF5    0.630       
IEIP2  0.707       
IEIP3  0.514       
MOT21  0.546       
MOT3   0.694       
MOT5   0.532       
MOT6   0.543       
MOT7   0.535       
MOT8   0.736       
MOT9   0.545       
AFP1          0.638
AFP2          0.700
AFP6          0.867
CF1           0.492
CF2                
CF3    0.409       
CF6           0.412
CF7    0.491       
CF8                
IEIP1              
IEIP4              
MOT1          0.434
MOT4               

                 PA1   PA2
SS loadings    6.570 2.689
Proportion Var 0.243 0.100
Cumulative Var 0.243 0.343

Diagramme

fa.diagram(fit2, digits = 2)

3 Facteurs

Modèle

fit3 <- fa(dataComp, nfactors = 3, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit3)
Factor Analysis using method =  pa
Call: fa(r = dataComp, nfactors = 3, rotate = "oblimin", fm = "pa", 
    use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix

                       PA1  PA2  PA3
SS loadings           5.68 3.34 2.06
Proportion Var        0.21 0.12 0.08
Cumulative Var        0.21 0.33 0.41
Proportion Explained  0.51 0.30 0.19
Cumulative Proportion 0.51 0.81 1.00

 With factor correlations of 
     PA1  PA2  PA3
PA1 1.00 0.48 0.43
PA2 0.48 1.00 0.32
PA3 0.43 0.32 1.00

Mean item complexity =  1.5
Test of the hypothesis that 3 factors are sufficient.

The degrees of freedom for the null model are  351  and the objective function was  12.18 with Chi Square of  2097.64
The degrees of freedom for the model are 273  and the objective function was  2.38 

The root mean square of the residuals (RMSR) is  0.05 
The df corrected root mean square of the residuals is  0.05 

The harmonic number of observations is  183 with the empirical chi square  300.36  with prob <  0.12 
The total number of observations was  183  with Likelihood Chi Square =  405.06  with prob <  3.5e-07 

Tucker Lewis Index of factoring reliability =  0.901
RMSEA index =  0.051  and the 90 % confidence intervals are  0.041 0.062
BIC =  -1017.13
Fit based upon off diagonal values = 0.98
Measures of factor score adequacy             
                                                   PA1  PA2  PA3
Correlation of (regression) scores with factors   0.95 0.93 0.85
Multiple R square of scores with factors          0.90 0.87 0.73
Minimum correlation of possible factor scores     0.81 0.75 0.46

Loadings

print(fit3$loadings, sort = T, cutoff = 0.4)

Loadings:
      PA1    PA2    PA3   
AFP3   0.502              
AFP4   0.734              
AFP5   0.578              
CF4    0.663              
IEIP2  0.536              
MOT3   0.633              
MOT6   0.567              
MOT8   0.815              
AFP1          0.675       
AFP2          0.689       
AFP6          0.863       
CF1           0.517       
MOT4                 0.545
CF2                       
CF3                       
CF5    0.480              
CF6           0.459       
CF7                  0.445
CF8                       
IEIP1                     
IEIP3                     
IEIP4                0.427
MOT1          0.433       
MOT21  0.457              
MOT5   0.402              
MOT7   0.485              
MOT9                      

                 PA1   PA2   PA3
SS loadings    4.909 2.808 1.542
Proportion Var 0.182 0.104 0.057
Cumulative Var 0.182 0.286 0.343

Diagramme

fa.diagram(fit3, digits = 2)

4 Facteurs

Modèle

fit4 <- fa(dataComp, nfactors = 4, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit4)
Factor Analysis using method =  pa
Call: fa(r = dataComp, nfactors = 4, rotate = "oblimin", fm = "pa", 
    use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix

                       PA3  PA1  PA2  PA4
SS loadings           3.89 3.85 2.95 1.14
Proportion Var        0.14 0.14 0.11 0.04
Cumulative Var        0.14 0.29 0.40 0.44
Proportion Explained  0.33 0.33 0.25 0.10
Cumulative Proportion 0.33 0.65 0.90 1.00

 With factor correlations of 
     PA3  PA1  PA2  PA4
PA3 1.00 0.59 0.43 0.24
PA1 0.59 1.00 0.38 0.32
PA2 0.43 0.38 1.00 0.21
PA4 0.24 0.32 0.21 1.00

Mean item complexity =  1.8
Test of the hypothesis that 4 factors are sufficient.

The degrees of freedom for the null model are  351  and the objective function was  12.18 with Chi Square of  2097.64
The degrees of freedom for the model are 249  and the objective function was  1.98 

The root mean square of the residuals (RMSR) is  0.04 
The df corrected root mean square of the residuals is  0.05 

The harmonic number of observations is  183 with the empirical chi square  221.97  with prob <  0.89 
The total number of observations was  183  with Likelihood Chi Square =  335.62  with prob <  2e-04 

Tucker Lewis Index of factoring reliability =  0.929
RMSEA index =  0.043  and the 90 % confidence intervals are  0.031 0.055
BIC =  -961.55
Fit based upon off diagonal values = 0.98
Measures of factor score adequacy             
                                                   PA3  PA1  PA2  PA4
Correlation of (regression) scores with factors   0.92 0.93 0.93 0.80
Multiple R square of scores with factors          0.85 0.87 0.87 0.64
Minimum correlation of possible factor scores     0.71 0.74 0.75 0.28

Loadings

print(fit4$loadings, sort = T, cutoff = 0.4)

Loadings:
      PA3    PA1    PA2    PA4   
CF7    0.626                     
MOT4   0.604                     
MOT9   0.501                     
AFP4          0.711              
AFP5          0.705              
MOT6          0.507              
MOT8          0.759              
AFP1                 0.631       
AFP2                 0.676       
AFP6                 0.865       
AFP3   0.417                     
CF1                  0.421       
CF2                              
CF3                              
CF4    0.429                     
CF5    0.499                     
CF6                              
CF8                              
IEIP1                       0.445
IEIP2  0.463                     
IEIP3  0.496                     
IEIP4  0.455                     
MOT1                 0.404       
MOT21         0.471              
MOT3          0.409              
MOT5                             
MOT7          0.410              

                 PA3   PA1   PA2   PA4
SS loadings    3.011 3.034 2.486 0.946
Proportion Var 0.112 0.112 0.092 0.035
Cumulative Var 0.112 0.224 0.316 0.351

Diagramme

fa.diagram(fit4, digits = 2)

5 Facteurs

Modèle

fit5 <- fa(dataComp, nfactors = 5, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit5)
Factor Analysis using method =  pa
Call: fa(r = dataComp, nfactors = 5, rotate = "oblimin", fm = "pa", 
    use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix

                       PA1  PA5  PA2  PA3  PA4
SS loadings           3.33 3.24 2.94 1.82 1.23
Proportion Var        0.12 0.12 0.11 0.07 0.05
Cumulative Var        0.12 0.24 0.35 0.42 0.46
Proportion Explained  0.27 0.26 0.23 0.14 0.10
Cumulative Proportion 0.27 0.52 0.76 0.90 1.00

 With factor correlations of 
     PA1  PA5  PA2  PA3  PA4
PA1 1.00 0.60 0.37 0.37 0.29
PA5 0.60 1.00 0.36 0.32 0.31
PA2 0.37 0.36 1.00 0.34 0.29
PA3 0.37 0.32 0.34 1.00 0.13
PA4 0.29 0.31 0.29 0.13 1.00

Mean item complexity =  2
Test of the hypothesis that 5 factors are sufficient.

The degrees of freedom for the null model are  351  and the objective function was  12.18 with Chi Square of  2097.64
The degrees of freedom for the model are 226  and the objective function was  1.65 

The root mean square of the residuals (RMSR) is  0.04 
The df corrected root mean square of the residuals is  0.04 

The harmonic number of observations is  183 with the empirical chi square  165.46  with prob <  1 
The total number of observations was  183  with Likelihood Chi Square =  277.81  with prob <  0.011 

Tucker Lewis Index of factoring reliability =  0.953
RMSEA index =  0.035  and the 90 % confidence intervals are  0.018 0.049
BIC =  -899.53
Fit based upon off diagonal values = 0.99
Measures of factor score adequacy             
                                                   PA1  PA5  PA2  PA3
Correlation of (regression) scores with factors   0.93 0.92 0.93 0.85
Multiple R square of scores with factors          0.86 0.85 0.87 0.71
Minimum correlation of possible factor scores     0.71 0.70 0.74 0.43
                                                   PA4
Correlation of (regression) scores with factors   0.82
Multiple R square of scores with factors          0.68
Minimum correlation of possible factor scores     0.35

Loadings

print(fit5$loadings, sort = T, cutoff = 0.4)

Loadings:
      PA1    PA5    PA2    PA3    PA4   
CF4    0.762                            
CF5    0.510                            
IEIP2  0.519                            
MOT9   0.540                            
AFP4          0.572                     
AFP5          0.657                     
MOT6          0.537                     
MOT8          0.746                     
AFP1                 0.651              
AFP2                 0.677              
AFP6                 0.838              
MOT4                        0.612       
IEIP1                              0.666
AFP3   0.438                            
CF1                  0.406              
CF2                                     
CF3                                     
CF6                  0.445              
CF7                         0.454       
CF8                                     
IEIP3  0.499                            
IEIP4                                   
MOT1                                    
MOT21         0.466                     
MOT3                                    
MOT5                                    
MOT7          0.404                     

                 PA1   PA5   PA2   PA3   PA4
SS loadings    2.417 2.472 2.459 1.352 1.001
Proportion Var 0.090 0.092 0.091 0.050 0.037
Cumulative Var 0.090 0.181 0.272 0.322 0.359

Diagramme

fa.diagram(fit5, digits = 2)

6 Facteurs

Modèle

fit6 <- fa(dataComp, nfactors = 6, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit6)
Factor Analysis using method =  pa
Call: fa(r = dataComp, nfactors = 6, rotate = "oblimin", fm = "pa", 
    use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix

                       PA5  PA1  PA2  PA3  PA6  PA4
SS loadings           3.36 3.30 2.66 1.42 1.28 1.23
Proportion Var        0.12 0.12 0.10 0.05 0.05 0.05
Cumulative Var        0.12 0.25 0.34 0.40 0.44 0.49
Proportion Explained  0.25 0.25 0.20 0.11 0.10 0.09
Cumulative Proportion 0.25 0.50 0.70 0.81 0.91 1.00

 With factor correlations of 
     PA5  PA1  PA2  PA3  PA6  PA4
PA5 1.00 0.58 0.34 0.30 0.21 0.30
PA1 0.58 1.00 0.37 0.34 0.25 0.31
PA2 0.34 0.37 1.00 0.21 0.34 0.27
PA3 0.30 0.34 0.21 1.00 0.17 0.05
PA6 0.21 0.25 0.34 0.17 1.00 0.18
PA4 0.30 0.31 0.27 0.05 0.18 1.00

Mean item complexity =  2
Test of the hypothesis that 6 factors are sufficient.

The degrees of freedom for the null model are  351  and the objective function was  12.18 with Chi Square of  2097.64
The degrees of freedom for the model are 204  and the objective function was  1.34 

The root mean square of the residuals (RMSR) is  0.03 
The df corrected root mean square of the residuals is  0.04 

The harmonic number of observations is  183 with the empirical chi square  114.56  with prob <  1 
The total number of observations was  183  with Likelihood Chi Square =  224.54  with prob <  0.15 

Tucker Lewis Index of factoring reliability =  0.979
RMSEA index =  0.023  and the 90 % confidence intervals are  0 0.041
BIC =  -838.19
Fit based upon off diagonal values = 0.99
Measures of factor score adequacy             
                                                   PA5  PA1  PA2  PA3
Correlation of (regression) scores with factors   0.92 0.93 0.93 0.82
Multiple R square of scores with factors          0.85 0.86 0.86 0.67
Minimum correlation of possible factor scores     0.71 0.72 0.71 0.34
                                                   PA6  PA4
Correlation of (regression) scores with factors   0.83 0.82
Multiple R square of scores with factors          0.69 0.68
Minimum correlation of possible factor scores     0.38 0.36

Loadings

print(fit6$loadings, sort = T, cutoff = 0.4)

Loadings:
      PA5    PA1    PA2    PA3    PA6    PA4   
AFP4   0.592                                   
AFP5   0.690                                   
MOT6   0.520                                   
MOT8   0.730                                   
CF4           0.684                            
IEIP3         0.514                            
MOT9          0.669                            
AFP1                 0.709                     
AFP2                 0.716                     
AFP6                 0.765                     
IEIP4                       0.612              
MOT1                               0.566       
IEIP1                                     0.674
AFP3          0.462                            
CF1                                            
CF2                                            
CF3                                            
CF5           0.486                            
CF6                                            
CF7                         0.466              
CF8                                            
IEIP2         0.451                            
MOT21  0.477                                   
MOT3                                           
MOT4                        0.435              
MOT5                                           
MOT7   0.423                                   

                 PA5   PA1   PA2   PA3   PA6   PA4
SS loadings    2.571 2.372 2.202 1.118 0.962 1.010
Proportion Var 0.095 0.088 0.082 0.041 0.036 0.037
Cumulative Var 0.095 0.183 0.265 0.306 0.342 0.379

Diagramme

fa.diagram(fit6, digits = 2)

7 Facteurs

Modèle

fit7 <- fa(dataComp, nfactors = 7, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit7)
Factor Analysis using method =  pa
Call: fa(r = dataComp, nfactors = 7, rotate = "oblimin", fm = "pa", 
    use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix

                       PA1  PA2  PA5  PA6  PA4  PA7  PA3
SS loadings           2.74 2.74 2.15 1.92 1.84 1.25 1.10
Proportion Var        0.10 0.10 0.08 0.07 0.07 0.05 0.04
Cumulative Var        0.10 0.20 0.28 0.35 0.42 0.47 0.51
Proportion Explained  0.20 0.20 0.16 0.14 0.13 0.09 0.08
Cumulative Proportion 0.20 0.40 0.55 0.69 0.83 0.92 1.00

 With factor correlations of 
     PA1  PA2  PA5  PA6  PA4  PA7  PA3
PA1 1.00 0.32 0.42 0.33 0.42 0.28 0.25
PA2 0.32 1.00 0.28 0.45 0.28 0.28 0.10
PA5 0.42 0.28 1.00 0.32 0.49 0.28 0.13
PA6 0.33 0.45 0.32 1.00 0.20 0.20 0.20
PA4 0.42 0.28 0.49 0.20 1.00 0.22 0.21
PA7 0.28 0.28 0.28 0.20 0.22 1.00 0.03
PA3 0.25 0.10 0.13 0.20 0.21 0.03 1.00

Mean item complexity =  2.5
Test of the hypothesis that 7 factors are sufficient.

The degrees of freedom for the null model are  351  and the objective function was  12.18 with Chi Square of  2097.64
The degrees of freedom for the model are 183  and the objective function was  1.15 

The root mean square of the residuals (RMSR) is  0.03 
The df corrected root mean square of the residuals is  0.04 

The harmonic number of observations is  183 with the empirical chi square  93.41  with prob <  1 
The total number of observations was  183  with Likelihood Chi Square =  192.94  with prob <  0.29 

Tucker Lewis Index of factoring reliability =  0.989
RMSEA index =  0.016  and the 90 % confidence intervals are  0 0.038
BIC =  -760.39
Fit based upon off diagonal values = 0.99
Measures of factor score adequacy             
                                                   PA1  PA2  PA5  PA6
Correlation of (regression) scores with factors   0.91 0.93 0.90 0.87
Multiple R square of scores with factors          0.83 0.86 0.82 0.76
Minimum correlation of possible factor scores     0.67 0.72 0.64 0.51
                                                   PA4  PA7  PA3
Correlation of (regression) scores with factors   0.87 0.82 0.80
Multiple R square of scores with factors          0.75 0.68 0.64
Minimum correlation of possible factor scores     0.50 0.35 0.29

Loadings

print(fit7$loadings, sort = T, cutoff = 0.4)

Loadings:
      PA1    PA2    PA5    PA6    PA4    PA7    PA3   
CF4    0.670                                          
MOT9   0.567                                          
AFP1          0.728                                   
AFP2          0.731                                   
AFP6          0.759                                   
MOT8                 0.777                            
MOT1                        0.643                     
AFP5                               0.612              
IEIP1                                     0.647       
IEIP4                                            0.651
AFP3   0.417                                          
AFP4                               0.474              
CF1                                                   
CF2                                                   
CF3                                                   
CF5    0.433                                          
CF6                                                   
CF7                                                   
CF8                                                   
IEIP2  0.439                                          
IEIP3  0.444                                          
MOT21                                                 
MOT3                                                  
MOT4                        0.469                     
MOT5                                                  
MOT6                                                  
MOT7                                                  

                 PA1   PA2   PA5   PA6   PA4   PA7   PA3
SS loadings    1.915 2.247 1.430 1.342 1.215 1.009 0.941
Proportion Var 0.071 0.083 0.053 0.050 0.045 0.037 0.035
Cumulative Var 0.071 0.154 0.207 0.257 0.302 0.339 0.374

Diagramme

fa.diagram(fit7, digits = 2)

Fiabilité

alpha(dataComp)

Reliability analysis   
Call: alpha(x = dataComp)

 

    95% confidence boundaries 

 Reliability if an item is dropped:

 Item statistics 

Non missing response frequency for each item
         1    2    3    4    5 miss
AFP1  0.02 0.08 0.50 0.24 0.16    0
AFP2  0.08 0.12 0.47 0.22 0.11    0
AFP3  0.01 0.05 0.15 0.34 0.46    0
AFP4  0.01 0.02 0.06 0.36 0.56    0
AFP5  0.01 0.02 0.10 0.28 0.58    0
AFP6  0.02 0.07 0.49 0.30 0.12    0
CF1   0.02 0.03 0.13 0.45 0.37    0
CF2   0.07 0.34 0.25 0.27 0.08    0
CF3   0.02 0.03 0.13 0.30 0.53    0
CF4   0.01 0.02 0.05 0.27 0.64    0
CF5   0.01 0.01 0.04 0.35 0.59    0
CF6   0.03 0.09 0.36 0.27 0.26    0
CF7   0.02 0.04 0.21 0.46 0.27    0
CF8   0.04 0.13 0.26 0.43 0.13    0
IEIP1 0.01 0.01 0.03 0.47 0.49    0
IEIP2 0.02 0.03 0.07 0.28 0.60    0
IEIP3 0.02 0.08 0.18 0.38 0.34    0
IEIP4 0.10 0.11 0.28 0.31 0.20    0
MOT1  0.02 0.08 0.46 0.30 0.14    0
MOT21 0.01 0.02 0.10 0.58 0.29    0
MOT3  0.01 0.02 0.04 0.50 0.44    0
MOT4  0.04 0.10 0.40 0.30 0.16    0
MOT5  0.01 0.04 0.22 0.48 0.25    0
MOT6  0.02 0.00 0.02 0.26 0.70    0
MOT7  0.01 0.01 0.09 0.46 0.44    0
MOT8  0.01 0.01 0.01 0.29 0.69    0
MOT9  0.03 0.02 0.16 0.39 0.40    0
---
title: "Analyse Factorielle Exploratoire"
output: 
  html_notebook: 
    toc: yes
    theme: spacelab
---



```{r}
library(tidyverse)  # Manipulation des données
library(readxl)     # Lecture des fichiers Excel
library(ggpubr)     # Représentations graphiques
library(rstatix)    # Tests statistiques en langage Dplyr
library(corrplot)   # Corrélogrammes
library(plotly)     # Graphes intéractifs
library(psych)
library(EFAtools)
library(shiny)
```


# Avec toutes les variables quantitatives {.tabset}

## Données

```{r echo=FALSE}
data <- read_excel("data/data_ubs.xlsx", sheet = "data_afm")
data$ID <- as.factor(data$ID)
data$Pays <- as.factor(data$Pays)
data$Poste <- as.factor(data$Poste)
data$Region <- as.factor(data$Region)
data$Experience <- as.factor(data$Experience)
data$Age <- as.factor(data$Age)
data$Sexe <- as.factor(data$Sexe)
data$Experience <- as.factor(data$Experience)
data$Type <- as.factor(data$Type)

data <- data %>%
  select(-C2, -C3, -C4.1,	-C4.2, -C4.3, -C4.4, -C4.5, -C4.6, -C4.7, -C4.8, -C4.9, 
         -Type, -Pays, -Sexe, 
         -Region,
         -Poste,
         -Experience,
         -Age,
         -INTU1)

data <- column_to_rownames(data, "ID")

dataComp <- data %>%
  drop_na()

dataComp
```

## Pré-requis

### Bartlett

```{r}
bartlett.test(dataComp %>% select(where(is.numeric)))
```

### KMO

```{r}
KMO(dataComp %>% select(where(is.numeric)))
```

## Nombre de facteurs

```{r}
fa.parallel(dataComp, fa="fa", fm="pa")
```

## Modélisation {.tabset}

### 2 Facteurs {.tabset}

#### Modèle

```{r}
fit2 <- fa(dataComp, nfactors = 2, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit2)

```


#### Loadings

```{r}
print(fit2$loadings, sort = T, cutoff = 0.4)
```

#### Diagramme

```{r}
fa.diagram(fit2, digits = 2)
```

### 3 Facteurs {.tabset}

#### Modèle

```{r}
fit3 <- fa(dataComp, nfactors = 3, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit3)

```


#### Loadings

```{r}
print(fit3$loadings, sort = T, cutoff = 0.4)
```

#### Diagramme

```{r}
fa.diagram(fit3, digits = 2)
```

### 4 Facteurs {.tabset}

#### Modèle

```{r}
fit4 <- fa(dataComp, nfactors = 4, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit4)

```


#### Loadings

```{r}
print(fit4$loadings, sort = T, cutoff = 0.4)
```

#### Diagramme

```{r}
fa.diagram(fit4, digits = 2)
```


### 5 Facteurs {.tabset}

#### Modèle

```{r}
fit5 <- fa(dataComp, nfactors = 5, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit5)

```


#### Loadings

```{r}
print(fit5$loadings, sort = T, cutoff = 0.4)
```

#### Diagramme

```{r}
fa.diagram(fit5, digits = 2)
```


### 6 Facteurs {.tabset}

#### Modèle

```{r}
fit6 <- fa(dataComp, nfactors = 6, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit6)

```


#### Loadings

```{r}
print(fit6$loadings, sort = T, cutoff = 0.4)
```

#### Diagramme

```{r}
fa.diagram(fit6, digits = 2)
```


### 7 Facteurs {.tabset}

#### Modèle

```{r}
fit7 <- fa(dataComp, nfactors = 7, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit7)

```


#### Loadings

```{r}
print(fit7$loadings, sort = T, cutoff = 0.4)
```

#### Diagramme

```{r}
fa.diagram(fit7, digits = 2)
```





## Fiabilité

```{r}
alpha(dataComp)
```



---


# Avec le retrait : AFE, NSUB, LDS {.tabset}

## Données

```{r echo=FALSE}
data <- read_excel("data/data_ubs.xlsx", sheet = "data_afm")
data$ID <- as.factor(data$ID)
data$Pays <- as.factor(data$Pays)
data$Poste <- as.factor(data$Poste)
data$Region <- as.factor(data$Region)
data$Experience <- as.factor(data$Experience)
data$Age <- as.factor(data$Age)
data$Sexe <- as.factor(data$Sexe)
data$Experience <- as.factor(data$Experience)
data$Type <- as.factor(data$Type)

data <- data %>%
  select(-C2, -C3, -C4.1,	-C4.2, -C4.3, -C4.4, -C4.5, -C4.6, -C4.7, -C4.8, -C4.9, 
         -Type, -Pays, -Sexe, 
         -AFE1, -AFE2, -AFE4, -AFE5,
         -NSUB1, -NSUB2, -NSUB3, -NSUB4, -NSUB5,
         -LDS1, -LDS2, -LDS3, -LDS4, -LDS5, -LDS6, 
         -Region,
         -Poste,
         -Experience,
         -Age, 
         -INTU1)

data <- column_to_rownames(data, "ID")

dataComp <- data %>%
  drop_na()

dataComp
```

## Pré-requis

### Bartlett

```{r}
bartlett.test(dataComp %>% select(where(is.numeric)))
```

### KMO

```{r}
KMO(dataComp %>% select(where(is.numeric)))
```

## Nombre de facteurs

```{r}
fa.parallel(dataComp, fa="fa", fm="pa")
```

## Modélisation {.tabset}

### 2 Facteurs {.tabset}

#### Modèle

```{r}
fit2 <- fa(dataComp, nfactors = 2, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit2)

```


#### Loadings

```{r}
print(fit2$loadings, sort = T, cutoff = 0.4)
```

#### Diagramme

```{r}
fa.diagram(fit2, digits = 2)
```

### 3 Facteurs {.tabset}

#### Modèle

```{r}
fit3 <- fa(dataComp, nfactors = 3, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit3)

```


#### Loadings

```{r}
print(fit3$loadings, sort = T, cutoff = 0.4)
```

#### Diagramme

```{r}
fa.diagram(fit3, digits = 2)
```

### 4 Facteurs {.tabset}

#### Modèle

```{r}
fit4 <- fa(dataComp, nfactors = 4, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit4)

```


#### Loadings

```{r}
print(fit4$loadings, sort = T, cutoff = 0.4)
```

#### Diagramme

```{r}
fa.diagram(fit4, digits = 2)
```


### 5 Facteurs {.tabset}

#### Modèle

```{r}
fit5 <- fa(dataComp, nfactors = 5, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit5)

```


#### Loadings

```{r}
print(fit5$loadings, sort = T, cutoff = 0.4)
```

#### Diagramme

```{r}
fa.diagram(fit5, digits = 2)
```


### 6 Facteurs {.tabset}

#### Modèle

```{r}
fit6 <- fa(dataComp, nfactors = 6, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit6)

```


#### Loadings

```{r}
print(fit6$loadings, sort = T, cutoff = 0.4)
```

#### Diagramme

```{r}
fa.diagram(fit6, digits = 2)
```


### 7 Facteurs {.tabset}

#### Modèle

```{r}
fit7 <- fa(dataComp, nfactors = 7, rotate = "oblimin", fm = "pa", use = "pairwise")

print(fit7)

```


#### Loadings

```{r}
print(fit7$loadings, sort = T, cutoff = 0.4)
```

#### Diagramme

```{r}
fa.diagram(fit7, digits = 2)
```





## Fiabilité

```{r}
alpha(dataComp)
```

